SOME RESULTS ON JACK’S LEMMA FOR ANALYTIC FUNCTIONS

Abstract

In this paper, an upper bound will be found for the second coefficient in the Taylor expansion of the analytical function $p(z)$ using the Jack lemma. Also, the modulus of the angular derivative of the $I_{f}(z)=\frac{zp^{\prime }(z)}{p(z)}$ function on the unit disc will be estimated from below.